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Question
For the equation given below, find the value of ‘m’ so that the equation has equal roots. Also, find the solution of the equation:
x2 – (m + 2)x + (m + 5) = 0
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Solution
x2 – (m + 2)x + (m + 5) = 0
Here a = 1, b = – 4(m + 2) and c = m + 5
Given equation has equal roots
Then D = 0
`=>` b2 – 4ac = 0
`=>` [–(m + 2)]2 – 4(1)(m + 5) = 0
`=>` m2 + 4m + 4 – 4m – 20 = 0
`=>` m2 – 16 = 0
`=>` m2 = 16
`=>` m = ±4
Put value of m in given equation
x2 – 6x + 9 = 0 or x2 + 2x + 1 = 0
`=>` (x – 3)2 = 0 or (x + 1)2 = 0
`=>` x – 3 = 0 or x + 1 = 0
`=>` x = 3 or x = –1
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